VLBI、卫星网和地面网联合平差的数学模型

本文同时顾及地面网尺度系统误差和卫星网尺度系统误差对各自网点坐标的影响,对联合平差中常用的两种7参数转换模型:Bursa模型和Molodensky模型进行了分析比较,在此基础上,提出了一种新的7参数转换模型;建立了甚长基线(VLBI)、卫星网和地面网联合平差的数学模型,并用模拟数据进行了数值分析,得到了一些有益结论。

New Approaches to the Combination of Terrestrial Networks with Satellite Networks and VLBI Base Lines

In this paper, some analyses and comparisions have been made on the two widelyused transformation models: the bursa model and the Molodensky model, with the consi-deration of the effects of the systematic scale errors of both terrestrial and satellite networks.On the basis of it, an improved transformation model (named WTS model) with sevenparameters has been proposed. Considering the high scale accuracy of VLBI Base Lineswhose scale error can be neglected with respect to that of terres trial and satellite networks,two equivalent models for combing VLBI base lines, satellite network and terrestrial networkhave been developed, in which two scale bias parameters corresponding to the terrestrialnatwork and the satellite network respectively have been considered. Some numerical analyseshave been made using these models, and the results have been compared with the corres-ponding results obtained from the combined adjustment of terrestrial and satellite network.The main conclusions are as follows: As there exist significant scale biases both in the terrestrial network and the satellitenetwork, and the scale biases of each network affects its coordinates in a different way,the relative scale parameter of the existing transformation models with seven parameters,such as the Bursa model,the Moledensky model etc., cannot absorb the scale biases ofthe two networks completely, thus resulting in systematic biases of the estimated translationparameters. The WTS model put forward in this paper has the minimum biases of theestimted translation parameters compared with the well-known Bursa model and the Mo-lodensky model. The influences of the scale biases upon the translation parameters and the estimatedcoordinates of the terrestrial network cannot be eliminated in the combined adjustmentswith only terrestrial and satellite data. Therefore,extra observations with higt scale accuracyshould be added. Compared with terrestrial and satellite networks VLBI base lines can beused to provide the scale standard (its scale biases is regarded as zero) for both terrestri-al and satellite networks. By using the models presented in this paper, it is possible toobtain the unbiased estimators of the translation parameters and the two scale parametersof the sattellite network and terrestrial network as well as the three rotation parameters,so that the transformation of the terrestria1 newtork into the satellite geocentric systemcan be realized and the influnce of scale biases upon the coordinates of the terrestYial geo-datic network can be eliminated..